I am confused by your number 3. Edited for what I think you mean, and using NYC (high cost) and Tulsa (low cost) to make your example more vivid:
"Building more in [NYC] causes people to move [to NYC because now it's cheaper to live there,] which causes jobs to move [to NYC], which causes more housing to be unused in [Tulsa, which causes housing costs to drop in Tulsa]."
If my understanding is correct, then housing prices drop in NYC, and housing prices drop in Tulsa. Therefore, housing prices drop on a national level. But you say,
"...which means housing costs don't decrease significantly on a national level ..."
But clearly they do.
Unless you're saying that the average American's housing cost doesn't drop. That's possible; it's just Simpson's Paradox. Housing is cheaper in NYC than before, and housing is cheaper in Tulsa than before. But housing is more expensive in NYC than Tulsa. Because you now have a higher population ratio NYC:Tulsa, the average housing cost might not drop.
But I would argue that kind of "housing costs don't decrease" is misleading. If the price of both types of housing drop, and that leads people to choose more expensive housing because it's now more affordable, that's not the cost increasing. That's people spending more money for a higher quality/quantity of product.
For instance, suppose the quantity of all types of housing increases 50%, and the price per square foot drops 33.3%. Now, everyone gets 50% more square feet for the same price as before. The total expenditure on housing is the same, but housing is definitely cheaper. Any apartment size that was $1500 before is $1000 now. Any house size that was $3000 before is $2000 now.
Substitute "in New York instead of Tulsa" for "50% more square feet" and it's obvious the cost has dropped, which makes the quantity demanded increase.
The fact that people spent 100x as much on face masks in 2020 doesn't mean that the cost of face masks increased 100x. People just bought 100x as many of them because the benefits increased by 100x. It's the total amount spent on face masks that increased 100x.
It seems to me that your argument conflates two different senses of "cost." One, cost per unit of housing; second, total amount spent on housing. If the first decreases, the second can increase, decrease, or stay the same. But it's the first that's the important one for the argument. Because the issue is, does building more housing change the cost per unit.
Having said all this, it's possible that I've misunderstood your argument.
Perhaps your argument is that, with lots of new housing built in NYC, prices drop in NYC and Tulsa, but consumers of housing are not necessarily better off because (for instance) they might be "forced" to move from Tulsa to NYC, making them less happy than they would have been otherwise, despite the lower housing prices in both cities.
But that's a completely different argument.
That is my argument. That's the whole point! I just also don't think that it means prices necessarily go down in Tulsa (because people leaving for NYC shows up mainly as less c... (read more)
Scott Alexander posted this last month, arguing that building more in an area doesn't necessarily decrease local prices because it can cause more people to move in.
I see 3 levels of argument here, based on 1st, 2nd, and 3rd-order effects:
Position (3) has long been my view, and I thought I'd write a post explaining it a bit.
The problem in America isn't a lack of aggregate housing, it's houses not being where people want to live. Building more in those areas might seem like an obvious solution, but it wrongly assumes "where people want to live" is constant. If we instead consider that it could change, we need to consider what makes people move from an area with cheap housing to an area where it's expensive.
You can just ask people that, and they'll tell you: jobs. OK, so why are there better jobs in the expensive areas?
If you ask an economist, they'll probably say something about improved economic efficiency from people being closer together. I don't buy it, because it contradicts what I observe directly:
Yes, people in NYC and Silicon Valley get paid more on average, but I reject the assertion that wages reflect productivity or competence. If wages were high simply because aggregation improved efficiency, then we'd see a stronger correlation between density and wages, but the correlation of wages with housing prices and with wealth is stronger. In my experience and the experience of people I know, the dominant factor is how close you are to money. Wages in NYC are high because there are wealthy investors and corporate executives there.
Why, then, are those rich people in NYC? Because:
In this model, building more housing in Silicon Valley or NYC just leads to more competition for about the same total income from "good jobs", with that number determined by the amount of money there. That makes things better for rich people buying luxury services in expensive cities, and worse for other people. If you make housing cheap enough for many poor people to move in, the rich people might even leave because of that, decreasing the number of good jobs.
The solution, then, is not to build more in high-demand areas - it's to force demand to be spread out more.